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Minimizing Age of Incorrect Information for Unreliable Channel with Power Constraint

Yutao Chen, Anthony Ephremides

TL;DR

The paper investigates minimizing Age of Incorrect Information (AoII) for a multi-state Markov source communicating over an unreliable channel under a power constraint. It formulates the problem as a Constrained Markov Decision Process and proves that the optimal policy is a mixture of two deterministic threshold policies, with the mixing calibrated to meet the power budget. An efficient algorithm based on Relative Value Iteration, finite-state MDP approximation, and threshold-structure exploitation is developed to compute the optimal thresholds, the mixing coefficient, and the resulting AoII. Numerical results quantify AoII improvements over AoI-optimal policies and show how system parameters like p, p_s, and α influence policy structure and performance. The approach provides a practical framework for AoII-aware control in resource-constrained remote monitoring and control systems.

Abstract

Age of Incorrect Information (AoII) is a newly introduced performance metric that considers communication goals. Therefore, comparing with traditional performance metrics and the recently introduced metric - Age of Information (AoI), AoII achieves better performance in many real-life applications. However, the fundamental nature of AoII has been elusive so far. In this paper, we consider the AoII in a system where a transmitter sends updates about a multi-state Markovian source to a remote receiver through an unreliable channel. The communication goal is to minimize AoII subject to a power constraint. We cast the problem into a Constrained Markov Decision Process (CMDP) and prove that the optimal policy is a mixture of two deterministic threshold policies. Afterward, by leveraging the notion of Relative Value Iteration (RVI) and the structural properties of threshold policy, we propose an efficient algorithm to find the threshold policies as well as the mixing coefficient. Lastly, numerical results are laid out to highlight the performance of AoII-optimal policy.

Minimizing Age of Incorrect Information for Unreliable Channel with Power Constraint

TL;DR

The paper investigates minimizing Age of Incorrect Information (AoII) for a multi-state Markov source communicating over an unreliable channel under a power constraint. It formulates the problem as a Constrained Markov Decision Process and proves that the optimal policy is a mixture of two deterministic threshold policies, with the mixing calibrated to meet the power budget. An efficient algorithm based on Relative Value Iteration, finite-state MDP approximation, and threshold-structure exploitation is developed to compute the optimal thresholds, the mixing coefficient, and the resulting AoII. Numerical results quantify AoII improvements over AoI-optimal policies and show how system parameters like p, p_s, and α influence policy structure and performance. The approach provides a practical framework for AoII-aware control in resource-constrained remote monitoring and control systems.

Abstract

Age of Incorrect Information (AoII) is a newly introduced performance metric that considers communication goals. Therefore, comparing with traditional performance metrics and the recently introduced metric - Age of Information (AoI), AoII achieves better performance in many real-life applications. However, the fundamental nature of AoII has been elusive so far. In this paper, we consider the AoII in a system where a transmitter sends updates about a multi-state Markovian source to a remote receiver through an unreliable channel. The communication goal is to minimize AoII subject to a power constraint. We cast the problem into a Constrained Markov Decision Process (CMDP) and prove that the optimal policy is a mixture of two deterministic threshold policies. Afterward, by leveraging the notion of Relative Value Iteration (RVI) and the structural properties of threshold policy, we propose an efficient algorithm to find the threshold policies as well as the mixing coefficient. Lastly, numerical results are laid out to highlight the performance of AoII-optimal policy.

Paper Structure

This paper contains 28 sections, 9 theorems, 47 equations, 5 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Overview
  3. Communication Model
  4. Age of Incorrect Information
  5. System Dynamic
  6. Case 1
  7. Case 2
  8. Case 3
  9. Problem Formulation
  10. Problem Optimization
  11. Lagrangian Approach
  12. Structural Results
  13. Finite-State MDP Approximation
  14. Expected Transmission Rate
  15. Optimal Policy
  16. ...and 13 more sections

Key Result

Lemma 1

The estimated value function $V_{\nu}(x)$ is increasing in both $x_d$ and $x_{\Delta}$ at any iteration $\nu$.

Figures (5)

  • Figure 1: Illustrations of the Markovian source and the evolution of $d$.
  • Figure 2: A sample path of $\Delta_{AoII}(X_t,\hat{X}_t,t)$.
  • Figure 3: Illustrations of AoII-optimal policy and AoI-optimal policy. The truncation parameter in ASM$m=800$ and the tolerance in Bisection search$\xi=0.01$. RVI converges when the maximum difference between the results of two consecutive iterations is less than $\epsilon = 0.01$.
  • Figure : Improved Relative Value Iteration
  • Figure : Bisection Search

Theorems & Definitions (19)

  • Lemma 1: Monotonicity
  • Proposition 1: Structural properties
  • proof
  • Theorem 1: Convergence
  • proof
  • Proposition 2: Expected transmission rate
  • proof
  • Remark 1
  • Corollary 1: Approximation
  • proof
  • ...and 9 more